Hyperfine interactions of ${\mathrm{Er}}^{3+}$ ions in ${\mathrm{Y}}_2{\mathrm{SiO}}_5$: Electron paramagnetic resonance in a tunable microwave cavity

The hyperfine structure of the ground state of erbium-doped yttrium orthosilicate is analyzed with the use of electron paramagnetic resonance experiments in a tunable microwave resonator. This work was prompted by the disagreement between a recent measurement made at zero magnetic field and a previously published spin Hamiltonian. The ability to vary magnetic field strength, resonator frequency, and the orientation of our sample enabled us to monitor how the frequencies of hyperfine transitions change as a function of a vector magnetic field. We arrived at a different set of spin Hamiltonian parameters, which are also broadly consistent with the existing data. We discuss the reliability of our spin Hamiltonian parameters to make predictions outside the magnetic field and frequency regimes of our data. We also discuss why it proved to be difficult to determine spin Hamiltonian parameters for this material and present data collection strategies that improve the model reliability.

Figure 1

Experimental setup. (a) Photo of our tunable loop-gap resonator. Left, body of our cavity; right, a cap and a plunger. $y$ and $z$ indicate the corresponding directions of our magnetic field. (b) Schematic picture of the tunable resonator. The resonant frequency can be tuned by moving the plunger to change the gap $d$. Coordinate systems of our crystal and our magnetic field are also shown. (c) Schematic of the applied magnetic fields. Shown here is the scanning of $B_z$ for $B_x=10.3\mathrm{mT}$ and $B_y=0\mathrm{mT}$. (d) Typical EPR lines at three different resonator frequencies. The lines are vertically shifted for clarity.

Figure 2

Experimental EPR data and calculated transition lines. In the color plots, each horizontal slice is a normalized EPR spectrum as a function of $B_z$, while the applied $B_x$ and $B_y$ are indicated by the corresponding insets. (a) The measured EPR spectra at $\theta =64.{04}^{\circ }$. The scanned resonator frequency range is 3388.6 to 4975.6 MHz. (c) The measured EPR spectra at $\theta =104.{04}^{\circ }$. The scanned resonator frequency range is 3960.6 to 5058.8 MHz. (e) The measured EPR spectra at $\theta =84.{96}^{\circ }$. The scanned resonator frequency range is 3811.3 to 5184.8 MHz. (b), (d), and (f) The circle dots are the experimental EPR peaks extracted from (a), (c), and (e), respectively. On top of the experimental points, the purple lines are the EPR lines for site 1 from calculations using the parameters in Table 1, and blue lines are for site 2.

Figure 3

(a) Experimental zero-field EPR spectra reproduced from Ref. [8]. (b) Calculated zero-field EPR spectrum with spin Hamiltonian parameters in Table 1, which were obtained by fitting both the 2D EPR data and the zero-field EPR data. (c) Calculated zero-field EPR spectrum with spin Hamiltonian parameters, which are obtained by just fitting the 2D EPR data. The transition strengths of site 2 in (b) and (c) are much smaller than that of site 1; therefore for clarity the transitions from site 2 are not shown in (b) and (c). (d) Calculated zero-field EPR spectrum with spin Hamiltonian parameters in Ref. [14].

Figure 4

Angular variation in the (${\mathbf{D}}_{\mathbf{1}},{\mathbf{D}}_{\mathbf{2}}$) plane of eight allowed hyperfine transitions of site 2 at 9.5 GHz. Black spots and black lines are experimental points and fit curves adapted from Ref. [14]; the colored lines are transition lines based on spin Hamiltonian parameters in Table 1. Similar behavior was observed when comparing our spin Hamiltonian with other results from that study, except for one field rotation in the (${\mathbf{D}}_{\mathbf{2}},{\mathbf{b}}^{\prime }$) plane where we were unsure of the exact orientation used.